Nina Shokina

Simulation of surface waves generated by an underwater landslide in a bounded reservoir

Abstract Equations of a landslide motion over an uneven underwater slope subject to gravity and buoyancy forces, water friction and resistance are presented. A simulation of surface waves generated by a landslide in a bounded reservoir with a parabolic bottom profile has been performed within the nonlinear shallow water equations, and the results of that simulation are given. The influence of the parameters of the motion equation on the maximal splashing size is studied numerically.

On numerical modelling of impulse water waves generated by submarine landslides

An algorithm is presented for numerical modelling of impulse water waves generated by submarine landslides moving along irregular bottom profiles. A spatially nonuniform submarine landslide moving on a spatially nonuniform slope is modelled by a “quasi-deformed” rigid body. In addition, a simplified model is studied for the particular case of landslide and bottom profiles dependent on one spatial coordinate only. Both models are used for the comparative analysis of numerical and experimental data for submarine rigid landslides moving along a plane slope. The simplified model is applied to analyse the dependences of wave characteristics on various parameters for submarine landslides moving along a sea bottom slope with monotonically increasing depth and in a bounded reservoir. The full model is used to study the landslide trajectories and the wave patterns for the model submarine landslide of a spatially irregular shape moving in the model reservoir with a spatially irregular bottom. All numerical computations are performed using the nonlinear shallow water equations with moving bottom and the time-stepping algorithm provided by a predictor–corrector scheme on adaptive grids.

Simulation of tsunami waves generated by submarine landslides in the Black Sea

Abstract Numerical technique for studying surface waves appearing under the motion of a submarine landslide is discussed. This technique is based on the application of the model of a quasi-deformable landslide and two shallow water models, namely, the classic (dispersion free) one and the completely nonlinear dispersive model of the second hydrodynamic approximation. Numerical simulation of surface waves generated by a large model landslide on the continental slope of the Black Sea near the Russian coast is performed. It is shown that the dispersion has a significant impact on the picture of propagation of tsunami waves on sufficiently long paths.

Numerical Modelling of Surface Water Waves Arising Due to Movement of Underwater Landslide on Irregular Bottom Slope

The work is devoted to the numerical modelling of surface water waves generated by a moving underwater landslide on irregular bottom. Currently the works of other authors consider flat bottoms only. The modelling is done in the framework of the shallow water model with taking into account bottom mobility. The equations are obtained for an underwater landslide movement under the action of gravity force, buoyancy force, friction force and water resistance force. The predictor-corrector scheme [5], preserving the monotonicity of the numerical solution profiles in a linear case, is used on adaptive grids, which are generated using the equidistribution method [7]. The scheme is tested for the problem with a known analytical solution, describing the wave generation by a nondeformable body, which moves with a constant velocity on a horizontal bottom. The analysis is done for an irregular bottom of the dependencies of wave regime characteristics on bottom slope, initial landslide depth, its length and width.

Advances in High Performance Computing and Computational Sciences

Solution of Maxwells equations on partially unstructured meshes.- The integral equations method in problems of electrical sounding.- The chain of abstraction in High Performance Computing and simulation.- 3D Euler flow simulation in hydro turbines: unsteady analysis and automatic design.- On parallelization of one 3D fluid flow simulation code.- Development of algorithm for visualization of results in scientific research.- A general object oriented framework for discretizing non-linear evolution equations.- The Cauchy problem for Laplace equation on the plane.- Challenges of future hardware development and consequences for numerical algorithms.- Simulation of flame propagation in closed vessel with obstacles.- Detailed numerical simulation of the auto-ignition of liquid fuel droplets.- Numerical investigation of a supersonic flow with jet injection.- Object-oriented framework for parallel smoothed particle hydrodynamics simulations.- Numerical calculation of industrial problems.- Large-eddy simulations for tundish and airfoil flows.- Solution of one mixed problem for equation of relaxational filtration by Monte Carlo methods.- Numerical prediction of vortex instabilities in turbomachinery.

Adaptive modelling of coupled hydrological processes with application in water management

This paper presents recent results of a network project aiming at the modelling and simulation of coupled surface and subsurface flows. In particular, a discontinuous Galerkin method for the shallow water equations has been developed which includes a special treatment of wetting and drying. A robust solver for saturated–unsaturated groundwater flow in homogeneous soil is at hand, which, by domain decomposition techniques, can be reused as a subdomain solver for flow in heterogeneous soil. Coupling of surface and subsurface processes is implemented based on a heterogeneous nonlinear Dirichlet–Neumann method, using the dune-grid-glue module in the numerics software DUNE.

Adaptive modelling of two-dimensional shallow water flows with wetting and drying

The current work is done in the framework of the BMBF (Bundesministerium fur Bildung und Forschung - the Federal Ministry of Education and Research) project AdaptHydroMod - Adaptive Hydrological Modelling with Application in Water Industry [1], which is devoted to the development of generic adaptive approach to modelling of coupled hydrological processes: surface and groundwater flows. The surface water flow is modelled by the two-dimensional shallow water equations and the surface flow - by the Richards equation. The implementation is based within DUNE - the Distributed and Unified Numerics Environment [14]. The surface flow, on which we focus in the presented paper, is numerically solved using the Runge-Kutta discontinuous Galerkin method [10] with modifications to render the scheme well-balanced and for handling correctly possible wetting and drying processes. The newly developed limiter [12] is used for the stabilization of the method. The validation of the code is done using several test problems with known exact solutions. The problem with a mass source term, which is a first step to the coupled simulation of the surface and groundwater flows, is solved numerically.

NUMERICAL MODELLING OF SURFACE WAVES IN THE FRAMEWORK OF THE SHALLOW WATER MODEL

An improved adaptive grid method is considered for the numerical solution of the problems on propagation and run-up of surface waves, described by the one-dimensional shallow water model. The modified algorithm for the realization of the explicit predictor-corrector scheme is presented, which is based on the new way of computation of the right-hand side of the shallow water equations. A new method for choosing the scheme parameters on the basis of the analysis of the differential approximation is suggested that guarantees the satisfaction of the TVD-property for the improved predictor-corrector scheme. The presented method for construction of different conservative schemes on moving grids is based on an appropriate choice of the scheme parameters for the predictor–corrector scheme, which represents the canonical form of the two-layer explicit schemes for the shallow water equations. The improved difference boundary conditions are obtained at the moving waterfront point using the known analytical solutions of the shallow water equations in the vicinity of a water-land boundary. These boundary conditions approximate the analytical solutions with a higher accuracy than the conditions used in the earlier works. The numerical results for the improved adaptive grid method are presented.